For what it’s worth, I actually think restricting that option in this scenario is entirely fair—while providing the option to push through your fear and enter the house anyway would be nice for certain MCs, it’s true that it complicate things in a number of ways. I can’t speak for others, but I’d personally be okay if knocking on the door was the furthest an animal-shy MC was allowed to go.
That being said, these are issues you’d run into at basically every step along the way with an animal-shy K romance, so I don’t know if this compromise would necessarily solve anything in the long run—I assume you’d still need to write different versions of a lot of K-related scenes depending on the MC’s attitude toward animals. Obviously, I’m not trying to talk you out of this—if it’s not apparent by now, this is a route I’d dearly love to see come to fruition—but it is something to consider if you’re thinking about implementing this idea later on as opposed to now.